Design and Development of an Auto-Steering System Control for Off-Road Vehicles

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Design and Development of an Auto-Steering System

Control for Off-Road Vehicles

Ehsan Kiani

Submitted to the

Institute of Graduate Studies and Research

in partial fulfillment of the requirements for the Degree of

Doctor of Philosophy

in

Mechanical Engineering

Eastern Mediterranean University

September 2012

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Approval of the Institute of Graduate Studies and Research

Prof. Dr. Elvan Yılmaz Director

I certify that this thesis satisfies the requirements as a thesis for the degree of Doctor of

Philosophy in Mechanical Engineering.

Assoc. Prof. Dr. Ugur Atikol

Chair, Department of Mechanical Engineering

We certify that we have read this thesis and that in our opinion it is fully adequate in scope and quality as a thesis for the degree of Doctor of Philosophy in Mechanical Engineering.

Asst. Prof. Dr. Mehmet Bodur Asst. Prof. Dr. Hasan Hacisevki Co-Supervisor Supervisor

Examining Committee 1. Prof. Dr. Majid Hashemipour

2. Asst. Prof. Dr. Mehmet Bodur 3. Asst. Prof. Dr. Neriman Özada 4. Asst. Prof. Dr. Selim Solmaz 5. Asst. Prof. Dr. Hasan Hacışevki

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ABSTRACT

In this thesis, a control method is developed to enhance the path tracking accuracy of an agricultural vehicle steering system. Therefore, in order to boost the mean error value, the lateral error of a farm tractor at the curvature transitions is minimized by introducing a second look-ahead reference point (LARP) to the conventional lateral deviation controller. Since automation and precision have been significant objectives in the recent studies of land vehicle guidance controllers, a reasonable trade-off has been sought to come up with a steering control system approach with respect to the modern farming operation needs, recent industrial developments, sophistication degree of the approach, reliability, manoeuvrability, accuracy, computational cost, implementation feasibility and sensitivity to variation of system parameters.

Present study develops a simple automatic path tracking system to satisfy the typical requirements of an unmanned agricultural tractor application based on properties of two look-ahead reference points (LARPs) on the desired path. The main objective of the proposed control system is to track the desired path within reasonable tolerances of a typical farming process including considerable slippage.

Since the path shape of the farm field depends strongly on the terrain and surrounding environment such as crop rows pattern, the curvature of the reference path is subject to change. Thus, the employed look-ahead reference points provide compensation for centrifugal forces and reduction of the peak lateral deviation due to curvature transition, using only simple arithmetic operations.

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Extensive numerical tests were carried out on the computer simulation of the system dynamics driven by the proposed control method. Simulation results indicate enhancements in vehicle manoeuvrability and reduction of peak lateral displacement error at the curvature transitions to one fifth of single LARP error.

The proposed 2-LARP control strategy performs exactly same as the conventional lateral deviation controller on the linear and circular paths but it outperforms the conventional controller at the curvature transitions where the second LARP behaves independent to the first LARP.

Keywords: look-ahead reference point (LARP) control, path tracking, automatic steering agricultural vehicle, curvature transition.

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ÖZ

Bu çalışmada dairesel dönüş yapan tarımsal traktör aracının yanal hatalarının ikinci ileri görüş referans noktasının (LARP) konvansiyonel yatay sapma kontrolörüne ilave edilmesi ile en aza indirilmesi sağlanmıştır. Otomasyon ve hassasiyet son zamanlarda arazi araçları kontrolünde önemini artırdığından direksiyon kontrolünde hatırı sayılır ticari değer artışları gözlemlenmiştir. Modern tarım operasyonları olaya yaklaşım derecesi ve endüstrideki son gelişmeler da dikkate alınarak dayanıklılık, manevra kabiliyeti, doğruluk, bilsayar fiyatı, uygulanabilirlik fizibilitesi, ve hassasiyet parametrelerinin değişim derecesi bunu daha önemli kılmaktadır.

Bu çalışmada insansız tarım aracından beklenen tipik uygulamaları sağlamak için iki ileri görüş referans noktasını (LARP) özelliklerini kullanarak basit otomatik yol takip sistemi geliştirilmiştir. Önerilen control sisteminin ana konusu, tipik tarımsal prosesler için arzu edilen yolun makul kaymalar ve kabul edilebilir tolerenslar dahilinde alınmasıdır.

Bir tarım arazisinin yol şekli kuvvetle tarım arazisinin bölge ve çevresine bağlıdır, örneğin ürün sıra şekline, bu yüzden referans noktasın kavisi her harekette değişime uğramaktadır. Sadece basit aritmetik operasyonlar kullanarak atanmış ileri bakış referans noktalarının merkezkaç kuvvetlerin dengelenmesi ve pik yatay sapmaların azalması kavis geçiş ile sağlanmaktadır.

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System dinamikleri simülasyonu üzerine önerilen control metodu ile ilgili olarak çok miktarda bilgisayar destekli numerik çalışma yapılmıştır. Simülasyon neticeleri araç manevra kabiliyetinde artış olduğunu göstermiştir. Testler araç yanal kayma hata miktarının kavis taşıması sırasında tek ileri bakış açısına gore beş kez daha az olduğunu göstermistir.

Önerilen çift ileri bakış referans noktası (2-LARP) control stratejisi kullanılan konvansıyonel yatay sapmalı kontroler ile düz ve virajlı yollarda tamamen ayni neticeyi vermiştir, fakat konvansiyonel kontroler kavis geçişlerinde daha az başarılıdır, ikinci ileri bakış referans noktası birinci ileri bakış referans noktasına göre daha bağımsız davmanktadır.

Anahtar Kelimeler: ileriye bakış referans noktası (LARP) kontrolü, yol takibi,

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ACKNOWLEDGMENT

First of all I thank God for giving the strength and potential, guidance opportunity to pursue the present study up to a certain level. I should thank my parents for growing the science passion as well as their sacrifice and pushing me whenever disappointed. “Son! No guts no glory” my parents often remind me. Moreover, Uncle Mick for his generous supports.

I should thank many people without whom I could not progress this project; first, my supervisors, Asst. Prof. Dr Mehmet Bodur to his guidelines, technical ideas and scientific helps and also Asst. Prof. Dr. Hasan Hacışevki for h is continu ou s encouragements.

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LIST OF TABLES

Table 1: Verification parameters of CLAAS Renault ARES 640 ... 71

Table 2: Simulation Parameters of John Deere 8420 ... 71

Table 3: Optimization conditions, optimum parameters, and resulted errors ... 80

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LIST OF FIGURES

Figure 1. Side view of a typical agricultural vehicle with implement for material

spreading dynamics having controller and position-sensor unit ... 32

Figure 2. Top view of a typical agricultural vehicle showing the symbols related to the vehicle kinematics ... 36

Figure 3. Bike model of vehicle as three degrees of freedom (3DOF) model with its definition of symbols ... 37

Figure 4. Definition of symbols on a) The 3-DOF vehicle model, and b) The front tyre. ... 38

Figure 5. Architecture of the simulation platform for the automatic tracking control system and vehicle dynamics. ... 41

Figure 6. Block diagram of 2-LARP Control Unit ... 42

Figure 7. Source of a disturbance force while a tyre passes over a slope. Front view of vehicle. ... 44

Figure 8. Source of a disturbance force while a tyre passes over a slope. Front view of tyre on the soil clod... 45

Figure 9: Schematic model of the actuator used for this study ... 46

Figure 10. Path tracking specifications ... 48

Figure 11: The relation between K1 and L1 with RMS error values ... 55

Figure 12: The relation between K1 and L1 with peak error values ... 55

Figure 13. Top view of the test path to observe the performance of the controller……. 59

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Figure 15. Step response of lateral error control for minimum dN,RMSE case without using

LARP. The amplitude of the applied step is 0.1 m. The peak and opposite peak points are marked by a and b. ... 62 Figure 16. Root locus plot for the overall system. The circle marks the zero, and the crosses are the poles of the system with the minimum dN,RMSE along a 0.1 m step

response. ... 62 Figure 17. Root locus plot of the poles caused by the controller parameters found in the third step, non-constrained search for best peak lateral error. ... 64 Figure 18. Step response of the linear system from the controller parameters found in the third step, non-constrained search for best peak lateral error. ... 64 Figure 19. Schematic flowchart of the third and forth steps of optimization algorithm . 66 Figure 20. Lateral displacements of the systems with the best parameters for case b (dotted line) and for case (d) along the test path with 7 m circular section from s=10 to s=32. The peak and opposite peak points are marked by a and b. ... 68 Figure 21. Comparison of the lateral errors. ... 72 Figure 22. Relation between lateral deviation and orientation deviation gains with peak value of the lateral error. ... 73 Figure 23. Relation between lateral deviation and orientation deviation gains with RMSE value of the lateral error... 74 Figure 24. Relation between look ahead point distances, l1 and l2 with peak values of the

lateral error, while kd = kN = k1 = k2 =1. ... 75

Figure 25. Relation between look ahead point distances, l1 and l2 with RMSE values of

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Figure 26. Centrifugal force compensation tests on a circular path of ρ= 7 m, with K1= 0, Kd = 0.6, and K0 = 2 – K2c , for four cases of K2c , (a) K2c = 0,

(b) K2c = 0.5, (c) K2c = 0.8, (d) K2c = 1.0... 76

Figure 27. Effect of second LARP distance on the peak lateral deviation dN, peak ; the

solid curve is for 8 kmh-1 and the dashed curve is for 11 kmh-1 forward speeds. ... 77 Figure 28. Effect of second LARP distance on the mean lateral deviation, dN, RMSE ; the

solid line is for 8 kmh-1 , and the dashed line is for 11 kmh-1 forward speed. ... 77 Figure 29. Step response of the disturbance-free system to 2.5 m initial deviation, travelling over soil profiles with different grip conditions. ... 78 Figure 30. Step response of the closed loop system with dN = 1 m initial lateral deviation

for controller settings KN1= 2.0, (K1= K2= 0) and (a) Kd1= 0.4, (b) Kd1= 0.6 (c) Kd1=

0.8. ... 79 Figure 31. Schematic illustration for frequency response of lateral deviation in linear system transfer function ... 81 Figure 32. Schematic illustration for frequency response of orientation deviation in linear system transfer function ... 81

Figure 33. Root locus plot for lateral deviation gain variation along the linear path with KN = 1. ... 82

Figure 34. Steering angle δ (solid line), δdes (dashed line), δdis (dotted line). Dotted lines

are obtained with disturbance parameters used in the verification tests. ... 83 Figure 35. Lateral deviation dN (solid line), dN, dis (dotted line) measured at 8 km h-1.

Dotted lines are obtained with disturbance parameters used in the verification tests. .... 84 Figure 36. Tracking accuracy comparison of the Proposed 2-LARP method and results reported by Lenain et al. (2006). ... 84

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Figure 37. Vehicle side slip angle. ... 85 Figure 38. Front tyre slip angles

α

_f (solid) without disturbances, and

α

_f_,dis (dotted) with disturbances. ... 86 Figure 39. Lateral deviation, d , for velocities 5, 6.5 and 8 km h_N -1. ... 87 Figure 40. Lateral deviation error cause by change in second LARP distance having constant velocity of 8 km/h ... 88 Figure 41. Lateral deviation error cause by change in second LARP distance having constant velocity of 11 km/h ... 88 Figure 42. Lateral deviation error cause by change in 2-LARP forward velocity ... 89 Figure 43. Centrifugal Force versus second LARP distance variation ... 89

Figure 44. Graphical demonstration for estimated agricultural performance comparison ... 91

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LIST OF SYMBOLS

αf , αr (rad) Front and rear tyre slip angles NG

zero-mean unity-variance Gaussian distributed random number

β (rad) Vehicle side slip angle IZ (kg m)

Vehicle mass moment of inertia

∆spo (m)

Curvilinear distance between dN,peak and opposite dN,peak.

K1, K2

Controller coefficients for LARP tangent deviation δ (rad) Front tyre steer angle Kd, KN

Controller coefficient for lateral and tangent angle deviation

ψ (rad) Vehicle heading angle l (m) Wheel-base (=lf +lr)

ψi (rad)

Tangential direction of path point Pi

lf, lr (m)

Distances from vehicle centre of mass

ρ (m) Curved path radius L1, L2 (m)

Distances of look ahead reference points

Θi (rad)

Angular deviation from

vehicle heading LARP Look ahead reference point

aF, dis Extent of force disturbance LQR Linear Quadratic Regulator

aM, dis Extent of moment disturbance mveh (kg) Vehicle mass

CG Vehicle centre of gravity Mdis (N m) Disturbance moment

Cf , Cr

(N/rad) Cornering stiffness PW Mid-point of rear wheels

dN (m) Lateral deviation error PL1, PL2

Look ahead reference points

DOF Degree of freedom PN

Nearest point on the reference path to

EH Electro-hydraulic R (N) Rolling resistance

FC (N) Centrifugal force RMSE Root Mean Squared Error

FD (N) Propulsion force s (m) Curvilinear abscissa

Fdis (N)

Amplitude of disturbance

force v (m s

-1

) Vehicle actual velocity Ff , Fr (N) Cornering forces X, Y (m)

Global reference frame coordinates

Fy (N) Lateral Force XW,YW (m) Coordinates of

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Chapter 1 INTRODUCTION

1.1 Automation Significance in Modern Off-Road Operations

Modern off-road vehicle operations such as agricultural field tasks require modern techniques and technologies. By the advent of modern technologies into the engineering practice, the advanced methods are implementable to enhance the efficiency of the field operation. Moreover, the efficiency of each farming task has been broken down into more precise divisions containing more details.

Modern agriculture requires advanced autonomous methods to augment productivity both quantitatively and qualitatively. To accomplish the farming tasks on a field with high efficiency many technologies must be incorporated. In addition, for the sake of energy and environment saving even a few percentages enhancement in efficiency can result in remarkable financial benefits.

Carful usage of new technologies in sensors, actuators and processors boosts efficiency and reliability by integration of the scientific developments into agricultural applications.

The automatic control of ground vehicle steering system typically requires integration of five different technologies as path planning, medium recognition, sensing and actuation intercourse, path tracking and obstacle avoidance. In the present study, a problem is

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addressed to be solved as follows. A given predefined path is assumed to be accurately followed subject to an unpaved terrain conditions. Admittedly, the materials developed within the present study will be used for further advancements in controller and modelling to boost the provided performance according to the research and industry realms tendencies. Therefore, the core of this dissertation is focused on the proposed controller and evaluation of its performance. In addition each part of the project concept is broken down into simple description in order to pave the way of future advancements and further utilizations for any interested reader.

Indeed, a farm vehicle must operate even more accurately than a mars rover because if a mars rover path following tasks results in 20 cm error, it might not be considered as a failure while the same error of a farm vehicle tire might damage the whole crop row, that is an absolute failure. In addition, using technologies such as sensors in the agriculture vehicle has more advantages compared with passenger car. First, an agricultural vehicle is usually very heavy and hence additional weight of a sensor setup can be considered negligible. Secondly, an agricultural vehicle is often a large machine compared to a typical passenger car and can provide power for external implements. Therefore, implementation of sensor or processing setup, does not affect the overall system. Thirdly, the price of an agricultural vehicle is typically higher than that of a passenger car, in as much as, implementation of technologies will not increase its overall price remarkably.

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1.2 Overview of the Problem and the Proposed Solution

Since the field for off-road operation varies according to the local climate and soil condition, etc., the shape of the off-road pattern can be irregular. Therefore, the geometric curve which represents the path to be followed may change several times during the operation. This study proposes a simple method to reduce the lateral deviation error at the aforementioned curvature transitions to boost the tracking accuracy.

1.3 Contributions of the Present Study to Science and Industry

• A novel control method is developed for automatic guidance of a typical agricultural vehicle. The proposed 2-LARP control was extended from the idea of look ahead guidance of mobile robots to satisfy the typical requirements of an off-road vehicle such as an agricultural tractor.

• The introduced control law for 2-LARP strategy employs simple arithmetic operations.

• Peak lateral error at curvature transitions is reduced by five times as compared to the results reported in the literature by a lateral deviation controller (Derrick and Bevly, 2008).

• The presented system serves the purpose of precision needed in agricultural harvesting as well as for farm automation which have been hot topics in the last three decades.

• Performance is enhanced to millimetres tracking accuracy so that the system outperforms a human driver to facilitate both farm automation and precision.

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• A software code has been generated (Appendix B) simulating real applications such as tracking a given desired path through a control method integrated into the steering dynamics and kinematics of an agricultural vehicle.

• Extensive numerical simulations were carried out to evaluate the system performance. The evaluation results of the overall system indicates stability and manoeuvrability enhancements.

• The introduced second LARP reduces the peak lateral error at curvature transitions to one fifth of to 1-LARP and thus it indicates the independent effect of each LARP on lateral and consequently nonexistence of an equilibrium point.

• The computational cost of the second LARP injection in the conventional lateral control law is sufficiently low. Indeed, computational times of 1-LARP and 2-LARP systems are almost the same.

• The proposed method performs the agricultural application such as spreading insecticides more satisfactory than the ones previously presented in the literature. It is mostly because of the error reduction at curvature transitions and simplicity of the control structure in response to the precision and agility advantages of the recent actuation and measurement technology.

• The presented system can be used for dead reckoning of an automatically steered land vehicle with low forward velocities with high capability of oscillation rejection. Hence, the developed method facilitates the automation and precision in off-road operations.

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Chapter 2

2. LITERATURE REVIEW

2.1 Automatic Off-Road Vehicle Guidance

The trend towards using accurate and safe methods for agricultural automatic guidance systems has led to numerous researches since the 1920s. Indeed, a proper Automatic Guidance Control approach optimizes the use of water, land, fertilizer and seed (Aghkhani and Abbaspour Fard 2009).

Agricultural tasks in the field are often accomplished while travelling along a path. Therefore, path tracking for agricultural purpose is often carried out as a tedious work for labour since the driver must repeatedly do the same task. Moreover, spreading fertilizer and poison in the field is hazardous for the farmer. Besides, cost of labour is getting more expensive so the use of automatic systems may be preferable. Hence, efforts have been dedicated to improve the performance of unmanned vehicles in path tracking tasks and various automatic methods and system descriptions have been presented thus far. In recent two decades, research efforts in the agricultural vehicle automation field were enriched by Owen since 1982. The dynamics of a tractor for the handling purpose was extensively studied and used in the later research in this area. The foundation was sufficiently to define a handling analysis framework of a mobile robot moving on an unpaved surface with non-severe manoeuvre. Although the focus of the aforementioned research was on the motion analysis of the farm vehicle, rather than the

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controller or guidance method evaluation, yet, the formulations have been used several times thus far and it has been benefitted the research on the farm machinery motion analysis. One may notice that, in the control of an agricultural vehicle the interests of farmers must be accounted and hence in the following, their main desirable aspects of agricultural vehicle controller will be enlisted as studied by Reid et al. (2000) and Li et al. (2009);

1- The agricultural environment is a biosystem with considerable degree of sensitivity to changes. The tasks with minimal damaging to the environment are seriously recommended. In other words, an agricultural background consists of parts such as soft and moist material over the ground surface, crop rows, hill–hole profiles and large sands or clods as well as soft tyre contact patches. In addition, the tyre air pressure is adjusted in such a way that it can pass smoothly over the surface irregularities. Indeed, it is strictly forbidden to have tyres sinkage into the soil or overlap with crops lanes.

2- Rather than the speed of operatio, the quality of work is on priority. The products of farming often will be eaten by people directly or indirectly after some food processing so that the farm products must be carefully seeded, harvested and treated. Indeed, high speed working on farm has no room of consideration whereas it is risky to harm the machine or the surrounding. The restrictions on farming are:

a. The high chassis of tractor that is prone to turn over by some sharp turns which are not unsafe for passenger cars.

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b. Beating the fruits, seeds or other usable parts of plants by the implement beyond the range of safety is likely undesired because it changes the product quality. Therefore, the speed of operation should be well set to have minimum unwanted damages.

c. Soil texture particles are the essential elements to form the plants bed. Fast travel on the soil by a heavy vehicle and dealing with by an implement is counterproductive.

d. Indeed, since in the automation of agricultural operation, the performance is evaluated according to the quality of the operation, poor outcomes will easily hardly damage the entire performance and even may fail it. The precision in agriculture is one the concepts that is recently received heavy attention by several authors, research institutes and farm machinery manufacturers, to provide the brief goals of precision farming in the industry, techniques and tools (Li et al. 2009).

3- Spreading of materials such as fertilizer as well as spraying insecticide liquids in a hasty fashion causes overlaps over uncovered surfaces on the farm field and it seriously reduces the efficiency. Whereas these years the environment saving carries high weight especially for the annual approval of the machinery company, time, price and efforts that has been dedicated to the precision and automatic farming is justifiable. Several authors and institutions have been joint and collaborated to put these concepts and techniques some steps forward (Bevly and Cobb 2010, Lenain 2007, Zhang 2004, Rovira Mas et al. 2010, Hellstrom and Ringdahl 2006, and Eaton et al. 2008).

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Apart from what a farm vehicle driver aims while working on the field, the farmer prefers not to face the matters and situations in which the followings may exist:

1- Spreading herbicide and fertiliser, generates an unhealthy atmosphere around the distributer for at least some minutes so that human working beside those are harmful (O’Conner 1997). Moreover, agricultural vehicle works over a surface full of irregularities. Farm tractor can easily turn over and this is often due to wrong prediction of the driver for future state of tractor motion. Statistically speaking, several reports were broadcasted regarding death of driver specially in the busy, hot , cold or frustrating situations.

2- Driver supposed to carry out the agricultural job for a certain amount of time consists of divisions which are very similar to each other. This phenomenon is so called “driver fatigue” is very common particularly in large field in the agricultural friendly lands of states in North America and Australia. Getting tired is the first step towards loss of accuracy as well as danger to crop products, fatal turn over which remarkably damages the machine, operator and surrounding (Rovira Mas et al. 2010).

3- The cost of the recruitment of labour is getting higher. In other words, employment of human elements has its own concerns that it not desirable such as salary, insurance and some official job which are tedious and costly procedures [Rovira 2010]. In addition, rollover of a tractor has caused the driver’s death. Hence, development of technologies and techniques to plan, design and manufacturing towards safe, reliable, cost-effective and accurate or in general an efficient configuration can substitute the

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traditional way of human operation especially for the operations which are recursive or repetitive. On the other hand, expertise and moral of human driver may affect the operation efficiency on the field where the reprocess of the farming is not feasible most likely.

4- Advancement of technologies needs corresponding compatible and robust efficient approaches particularly land vehicle guidance controllers to cooperate well with the computerized facilities. The life is getting computerized these days more and more and gradually it is handling even personal matters and farming is not an exception. Therefore, authors have been through new and more accurate strategies which are implementable since the required facilities are on the way with quite close to what is needed to have the maximum possible efficiency. Actually, in large fields with financially sufficient infrastructure, human operators are reduced unless for the supervisory of the operation and also keeping the margins of safety within an agricultural task (Lenain et al. 2007, and Zhang and Qiu 2004).

5- Last but not least, the degree of preciseness of a computerized machine is far better than human operator, if the enough underlying tools and data are provided. On the other hand, machine does not get frustrated and exhausted and thus the field job can be pursued in the conditions which might not be desired most probably e.g. dusty, fogy or herbicide spread area (Bevly 2001). Therefore, automatic methods are so much beneficial even though still farmers who have been used to conventional farming especially on the small lands. Consequently, the cost of auto-farming must be dealt besides the reliability and precision concerns.

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6- Advent of newly developed integrated methods such as real time kinematic global positioning system (RTK-GPS) and carrier phase differential global positioning system (CD-GPS) which provide centimetre accuracy as well as actuator advancements to carry out the controller actions over the machine and terrain (Fang et al. 2011).

The research on the agricultural robotics is kind of multidisciplinary channelling task whereas it deals with biosystems via a dynamic behaviour and mechanical aspects. Therefore, spectrum of research are widely varied from agricultural studies to electrical analysis. In the following it is tried to cover the major works which have been provide the foundation for the further studies on the agricultural robotics with concentration on the tracking control of the vehicle utilizing computerized methods.

This underlying structure that was built by O’Conner in Stanford University and were further developed through three other PhD projects. O’Connor research focused on the feasibility of CDGPS implementation on land vehicle for the purpose of a precise guidance on a perfect land (O’Conner 1997). For a centimetre level accuracy the overall experimental system performance was satisfactory inasmuch as to be adopted for real-time application. This work was almost the first extensive study towards the practical analysis of technology integration for the purpose of auto-farming as well as evaluation and estimation for feasibility of controller, sensor and actuator utilization in the land vehicle guidance in which precision and efficiency were addressed. On this basis, Bell commenced a study over auto-farming concept towards high-precision. Indeed, precision criterion has been altered within last decade whereas measurement devices were developed and communication technology has been advanced to provide higher

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precision and less inaccuracy. The sensor characteristics and noise plays very significant role in the navigation and in turn, affect the controller performance because decision making in presence of lag and disturbance is close to the unstable and poor response margins (Lenain, et al. 2007 and Bell, 2000). Bell, (2000) proved that an automatic system facilitated by electronic processor and data collector can work more precise than an expert human driver on straight line route. The system identification used of this study was the main platform for future modelling of non-severe manoeuvre of farm tractor. For GPS sensor outage and control of the yaw motion of a tractor with a towed implement for slightly higher velocities and larger bandwidth, an approach was presented through dead reckoning of automatically steered farm vehicle. The fundamentals presented in this study paved the way for further research for real system parameter variation and estimation techniques (Bevly, 2001). The system identification of the aforementioned system and the obtained preliminary modelling restrictions paved the way for the future studies on the automatic farm tractor path tracking in presence and absence of both high irregularities and towed implements. The extensive modelling studies and analysis in this research has been used thus far for online estimation and predictive control action for automatic trajectory and path following. Also the concepts of lateral local error feedback were detailed. Indeed, for online or offline satisfactory path tracking performance, efforts must be dedicated to virtually execute the control action on the simulation test bed up to the end of the route to observe the performance along the entire path. On the other hand, in the Bevly’s research the effect of yaw motion and yaw rate were highlighted and formulated to some extent. Although as it is mentioned before, the problem statements has been altered since the difficulties of the modern technology implementation has been resolved over last few years. Specifically

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speaking, thanks to the advancement via research endeavours deficiencies such as actuator preciseness and control GPS uncertainties, high lag, outage and noise has been treated (Rovira Mas, et al. 2008, and Fang, et al. 2011). Gartley, (2005) established a cascaded system to have online estimation by determining an adaptation gain. Single input single output (SISO) control configuration presented in this study attempted to well define the relations between different parameters of the tracking system, however the focus was on the yaw stabilizing the system especially in the presence of hitch loading and unknown disturbances. The frequency domain representation clearly shows some margins for the stability and verifies the correlations among system major input and output variables such as transfer functions of steer angle actuation and desired steer angle requested by controller, lateral local error and yaw rate as well as lateral velocities. The prediction calculations were pursued along the straight lines and still there were room for curved path tracking control problem. Derrick (2008), followed the previously mentioned study to get more precise and detailed results and continued the adaptation gain evaluation of a towed implement effect on the modelling and found deterministic ratios on the almost the same cascaded system configuration. One significant aspect of his work is that the actuator effect the system is precisely modelled by accurate closed loop system and indeed it shows how the system performance is restricted in the simulations. In other words, the actuator saturation can damage the optimum pre-set controller design by avoiding the simulation to reach a certain and negligible error whether as lateral or heading deviation (Derrick and Bevly, 2008). Step responses presented by implement applied and implement free vehicle systems on the actual agricultural field showed a more than conventional second order system response with

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satisfactory error convergence and minimal steady state error along the straight line tracking.

Another avenue of research which is still under development is commenced in the Lasmea University by a team of research with an integration of expertise in agriculture, mechatronics and electronics disciplines. The idea of the current research was inspired by the aforementioned study from kinematic and path planning point of view since it is progressing over a strong kinematic modelling and verification foundation (Lenain et al., 2005). The sliding parameters which are the essential element for vehicle motion is extensively studied and the stream of the above research can be straightforwardly observed via the materials they have published. Indeed, to come up with the idea of accurate control of a mobile robot system, they focused on the sliding phenomenon which was dealt since the linear and nonlinear regions cause remarkable discrepancies especially for an off-road vehicle that is moving over an unpaved terrain since an agricultural vehicle does not travel by severe manoeuvre since it must move in a careful fashion not to harm the surroundings. The flow of research in the latest years is focused on the feasibility of high precision tracking control of an agricultural vehicle while it move over the special conditions such as a path with curvature transition as well as a terrain having constant slope. In addition, it has been tried to construct a model predictive control that is to provide the future states of the vehicle having motion over a predefined path. Moreover, the automation was kept as a priority to prove that the effort has practical application and financial benefits for farmers and manufacturers. As a matter of fact, prediction is a key feature of simulation and, in order to create a good model for control prediction concerns, parameter identification is required. Thus, many

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studies thanks are carried out by authors and research institutes and manufacturer. The mentioned French team have been developing their studies beyond the conventional ranges of vehicle linearity and gradually attempted to find the a simple method to bring the traditional modelling in validity with the semi-steady cornering of an agricultural vehicle manoeuvre simply via the correction factors respectively on the corresponding circumstances such as path shapes or terrain change divisions. Furthermore, since the agricultural task on the field is a repetitive kind of task on the straight lines followed typically by a circular curve path to turn the back to the field at the field margins so that the U-turn definition presented in the aforementioned research as one the main research challenge for evaluation of the control response quality, stability and error zero-convergence. In the present study it was observed that tracking along a path with curvature transition introduces large peak deviation errors that in some special cases it might result in the system performance failure by divergence if the straight line controller design is applied. For resolving of the problem one may suggest to have variable control parameter that is possible for an intelligent system. The point is in the agricultural robotics the simple design is preferred since complex systems may require large computer capacities such as memory or high power processor (Rovira Mas et al. 2010). Polar kinematics used in mentioned French team’s works is beneficial and precise though the system complexity is high to some extent. Besides, the controller may require strong embedded processor and in many farm lands it is not reasonable since the facilities for some farmers are poor and limited such as having computer administrator to fix the processor in the case of hot working shut down due to high load computational tasks. In general, that research jobs presents a good understanding of orientation and lateral error along path with a shape changes that is typical for an agricultural

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application on the farm field with sufficient simulation and actual field experimental tests that verify the validity of their virtual modelling. Although the disturbances on the field might be troublesome while an accurate model of the system is sought, recently it is tried to have the field well ploughed in such a way that travel of the vehicle tyres besides the furrow traces is a sort of moving over a semi-smooth surface (Behrouzi Lar, 2006). There are some other significant research efforts towards the farm tractor automatic and precise path or trajectory tracking. In brief, Zhang and Qiu (2004) tried to not only model the system but also come with the new idea of the controlling the system by simple and practical method by using middle points of the pre-defined path that is discretely dictated by the remote sensor such as GPS. Another independent research is dedicated to the actuator behaviour analysis that is one the main characters to modify the agricultural behaviour.

Within the aforementioned studies the tracking performance has been improved and some more characteristics and aspects of vehicle modelling and guidance have been taken into account for different manoeuvres and path and terrain specifications.

In most predictive path tracking control algorithms, a look-ahead point is employed to describe the position and orientation of a vehicle at a future time instant (Ozguner et al., 1995; Hellstrom and Ringdahl, 2006; Zhang and Qiu, 2004). The work done by Ozguner, et al. (1995) is the preliminary step towards path preview information usage for outdoor non-holonomic mobile robots. What has been carried out within last two decade in which modern technology such as computer is invented and implemented in the industrial products has been robust and safe automation and enhancement in the

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operation precision (Reid, et al., 2000). Precision improvement has been of priority besides stability guarantee however still there is a room for more precise data collection and actuation. Indeed there are bunch of approaches for controlling the guidance of vehicle on the off-road terrain. Furthermore, using remote sensors serve the purpose of automatic path tracking quite satisfactory because off-road operation is being pursued while the weather is fine (not rainy or too much windy), especially agricultural operation is not allowed in the conditions which are not appropriate which means that the soil or crop might be deformed or damaged. Therefore, farm land offers a good environment or background for path tracking control whereas clear and open farm land in which a few machines transmit communication waves for position and orientation data.

The follow-the-carrot method is simple to apply to a human driver; however, it has several drawbacks in automatic path tracking, such as oscillatory behaviour with insufficient LARP distances and undesired corner cutting with longer LARP distances (Barton, 2001; Lundgren, 2003).

2.2 Feasibility Evaluation and Foundation

By the advancement of modern facilities, the tractor subsystems such as sensor and actuator were studied to drive a reliable model for off line system. An analytical representation was provided and also the characteristics of electro-hydraulic actuator were discussed (Rovira-Mas 2008). A model of an electro-hydraulic actuator is presented and the adaptation gain is obtained to adjust the modelling with the tractor real time dynamics and kinematics such as lateral tire force and lateral/yaw errors (Derrick, 2008). Some researches were dedicated to stereo-vision camera and laser scanner to

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localize the vehicle position and attitude with respect to the crop rows (Wang 2011, and Oscar, et al. 2007). The experiment with these systems were satisfactory ran however, certain circumstances were maintained such the field conditions to have a clear vision and it is not surely available in the actual situation in the farm environment. Integration of different approaches into GPS systems has improved the accuracy of position and attitude measurement of outdoor vehicles. Indeed an agricultural vehicle is aimed to pursue an operation over the field rather solely to successfully pass a division of a road. Therefore, even centimetre accuracy is significant for farmers, especially when during the operation, sensor outage takes place or uniform lines are sought for seeder rows (Lenain, et al. 2006). In the open lands like an agricultural field, using integrated GPS sensor has been prevalent because the shortcomings such as connection interruption are rare. Real time kinematic global positioning system is one of the most reliable and commonly-used sensor types that for precise tracking controls of out-door robots have been widely adopted. In one of the most recent research, Fang, et al. 2011, employed GPS dual frequency EPOCH 25 RTK GPS, with 710 mm accuracy and 10 Hz sampling frequency (Fang, et al. 2011). For this study, it has been assumed that the proposed method is implemented into the setup with commonly used subsystems and it is already considered that sensor and actuator properties can affect the system performance. Hence, for development of the simulation test bed, and use it as a platform for semi-experimental tests to evaluate the system performance, these characteristics are taken into account.

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2.3 Numerical Tests and Software Simulation; Aspects and Benefits

in Off-Road Operations

Iterative experimental work on the outdoor mobile robot and off-road terrain has special characters. First, it needs to take into account the controller aims to solve the tracking problem so that restrictions must be well identified and comprehended as well as the risks or failure-producing actions. In addition, characters of highly nonlinear systems cannot be straightforwardly predicted or it will be formulated with infinite number of iterations to find the actual optimum design of a controller. Moreover, the characteristics of the terrain likely varies as long as the experiment is being carried out several rounds so that either the system design or the surrounding surface (terrain soil surface) will be heavily deformed and this is a critical point which must not occur since the soil deformation damages the performance by compaction that results in closing of the water passages inasmuch as the water penetration takes longer than one hour (Behrouzi Lar, 2006) and it ruins the plant roots which in turn drastically damages the farming efficiency. Apart from that, if the surface characteristics are altered then the next experiment will not be on the same foundation as the previous one and hence a claim based on each specifications alters experimental set-up so that it is not very reliable though it might give satisfactory results in practice since there might be better setting or design if the same characters is kept.

In general, empirical field tests on farm applications are tedious, hazardous, and cost-ineffective. Simulation tests are not only cost-effective but also precisely observable, and they provide rapid estimation of the efficiency of proposed methods. Computer-based approaches are proper choices, even to estimate the economical returns to the

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farmers. In contrast to the passenger car driver, the objective of the agricultural vehicle driver is not only to stay in a lane but to also accurately track a desired path because the overall efficiency of farming depends on the tracking accuracy. Consequently, a series of experimental simulations can be carried out to verify the feasibility of a proposed system as well as to evaluate its performance.

Review of the previously studied related papers which are focused on the precise tracking control of an autonomous off-road vehicle indicates that before the real field experimental tests, a set of numerical iteration for the purpose of motion and state analysis were carried out to first crosscheck the feasibility and overall performance of designed system as well as estimation prior to field tests (Lenain et al. 2006, Bevly and Cobb 2010). Indeed, combination of simulation and real time tests saves the resources and reduces the costs of controller design (Lenain 2010 however the financial supports of the internationally well known research groups are sufficiently high for even prone to damage experiments since development of a system that is reliable and helps the universal move towards environment saving draws so much attention and encouragement (Aghkhani and Abbaspour Fard 2009). Nonetheless, it has been common to use the real field parameter values of the system which were previously obtained carefully in which same system characters existed or preliminary parameter tests were performed to search for the certain parameter values and their corresponding circumstances (Lenain et al. 2006 and 2007, Gartley 2005, Derrick 2008, Zhang and Qiu 2004, Fang et al. 2011). Nevertheless, the vehicle specifications such as tyre properties and wheel distances from the vehicle centre of gravity (CG), are significant in overall system performance evaluation, since manufacturers do not produce agricultural

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vehicles with broad range of specifications, the terrain characteristics effects in system responses carried more weights than tyre properties and wheel distances from the vehicle centre of gravity CG, in system parameter identification and system formulation (Bevly 2001, Zhang and Qiu 2004). Hence, the common practice for commencement of a project towards tracking control system design and development which is funded by a factory to manufacture a real prototype has been terrain parameters identification so that the soil surface was already addressed (Fang, 2011). Derrick (2008) and Lenain, et al. (2007) performed their tests in such a way that simulation tests and the real experiments executed close together and therefore, a comparison between them gives the correction gain to be applied in the simulations tests and bring the results closer to the actual tests. It should be noted that in the modelling of the system, the expected but unknown disturbances will be present and they affect the performance evaluation particularly if the results being compared to the disturbance and noise free test inasmuch as those unwanted inputs dominate the overall outcomes of the system and re-evaluation must be of high necessity (Chapters 3 and 4). Those simulations have been a computerized method to determine the expected results specially position and orientation errors as well as lateral acceleration and yaw rate (Fang et al. 2011, Bevly 2001, Gartley 2008). Simulation offers free tests to even visualize the probable outcomes of the vehicle states subject to the certain external loads and under specific circumstances. In this study it has been tried to use the simulation test environment to search for the optimum parameters since each test for track a pre-defined path does not take more than a fraction of a second using a conventional personal computer.

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As a matter of fact, although to obtain the precise values there is often a need for actual field experimental tests, to verify the performance of a proposed approach there is a solution as integration of both methods on the same simulation test platform.

The idea of peak lateral error reduction at curvature transition was suggested Lenain, et al. (2006). Within their experimentations they observed large peak error at curvature transition and suggested to improve the tracking accuracy of automatic agricultural vehicle guidance by reducing this error. Since the human driver looks for a distance ahead of the car and adjusts the steer angle according to the future desired steer angle on the reference path. Similar path preview approach of deviation angle was used by Lenain, et al (2006). Intuitively speaking, using human intention method within the context of control practice helps the stability even if it does provide high accuracy. This later issue was discussed in details in controller method chapter.

Furthermore, the pattern of the waypoint is often known in advance, from a top view image. Therefore, within this study it is assumed that the path is given and planned by a higher level controller.

2.4 Previous Significant Methods of Agricultural Vehicle Path

Tracking Control

Various automatic methods and system descriptions have been presented thus far to serve the purpose of following a reference trajectory keeping a desired behaviour as the criterion for performance evaluation. These methods enriched and guided the present

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study by inspiration of the idea of the proposed control strategy as well as providing a benchmark for the performance comparison.

One of the major streams of research on agricultural automatic guidance was based on sensor communication effects and feasibility of the guidance automation of land vehicles since 1995 by O’Connor at Stanford University. The research of O’Connor (1997), Bell (1999), Reid (2000) and Bevly (2001) were all devoted to the feasibility of a simple lateral deviation controller for autonomous agricultural tractor. Vehicle, sensor and actuation models were presented and circumstances were discussed. In addition the footsteps for controller development were taken by extensive research on automation of agricultural vehicle in North America (Reid et al., 2000), Japan (Torii, 2000) and Europe (Keicher and Seufert, 2000).

Many controller aspects were covered such as vehicle modelling, estimation, manoeuvrability and stability (Derrick and Bevly, 2009; Bell, 1999; O’Connor 1997). The focus has been on the lateral position and attitude control and stability specification of the system.

Zhang and Qiu (2004) presented a method as a basis for path preview information usage, in which look ahead point was addressed to be used for steering angle command. An intelligent navigation plan was designed and implemented on the real tractor and sufficient accuracy was obtained. The idea of path tracking control of an autonomous vehicle was inspired by the approach presented by Zhang and Qui (2004) in which for simulation real time kinematic (RTK) GPS is assumed for simulation and used in

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practice. In addition, navigation control along both straight and curved paths was aimed to achieve peak lateral error of 10 cm.

Structurally similar approaches were presented such as look-ahead point strategy for forest autonomous vehicle (Hellstrom and Ringdahl, 2006) predictive, smart and precise experimental approaches (Lenain et al., 2006), intelligent off-road systems (Rovira-Mas et al., 2010), prompt control using electro-hydraulic steering (Wu et al. 2001), farm tractor dynamics estimation (Gartley and Bevly, 2008) and stereovision-based off-set measurements (Wang et al., 2011).

The lateral peak error reduction at curvature transitions was suggested by Lenain, et al. (2006). They came up with a robust and precise system however experienced poor performance at curvature transition. This weakness motivated the present study to develop a method with less computational complexity and better behaviour whenever changes in curves occur.

2.5 Drawbacks of the Previously Presented Agricultural Tracking

Control Strategies

In the previous presented methods (section 2.4), several drawbacks were noticed as follows;

• Although fuzzy control is a good alternative for the human operator (by deriving his intention), it is prone to instability. A jump between two neighbour rule functions can destabilize the tracking behaviour presented in Moustris and Tzafestas (2005), and Wang, et al. (2011).

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• Actuator non-linear behaviour has been a complicated problem. Servo-feedback can solve this drawback however; on the other hand, a transfer function model is required to represent the possible outcomes in response to desired values (Rovira-Mas and Zhang, 2008).

• Surface laid cable, proposed by Aghkhani and Abbaspour-Far (2009) is an expensive approach and hence it lacks faming advantages of cost-effectiveness and applicability for a large farm field.

• Laser scanner resolution at night or in dusty fields is poor and can results in fatal tracking errors (Wang et al. 2011).

• GPS sensor communication outage is very common in off-road practice (Bevly, 2001) and thus an automatic simulation method is required.

• The degree of complexities in the structure of controllers as well as the comput ational inefficiency may make these methods inefficient for agricultural tasks.

• Large lateral peak errors at curvature transitions have reported by the results of the previous studies. Even advanced control methods have produced high overshoots in response to reference path shape change. In my knowledge, the effects of waypoint shape variation on an agricultural tracking behaviour have not been studied.

The fuzzy control instability and structure complexity problems have been solved by employing a look-ahead strategy (Zhang and Qiu, 2004), while stereovision-based (e.g., laser scanner, camera) drawbacks have been addressed via a CDGPS-based approach (Thuilot et al., 2002).

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Automatic guidance of an agricultural vehicle requires a combination of technologies, such as electro-hydraulic actuation, DGPS sensors, and embedded controller techniques. The main aim of such mechanisms is to facilitate high manoeuvrability and accurate localization of a farm tractor. An electro-hydraulic (EH) actuator is highly nonlinear, but linearization of the servo control loop is possible and improves the actuator accuracy. Therefore, both of these techniques have been taken into account when developing the proposed system. On the other hand, for path tracking on a variable shape route such as a U-turn, the error in the shape transition needs to be reduced.

2.6 Objective of This Study

2.6.1 Problem Statement

Reference path shape in the off-road applications depends on a pattern provided by the terrain conditions and environment surroundings. As an example, the crop rows of agricultural field may have irregular shape since they planned to be next to the watering canal or against the local slope of a hilly surface. Subsequently, the curve type of the reference path changes several times and curvature transitions will produce large peak lateral errors during vehicle path tracking mission. Even existing advanced control methods produce large peak error at curvature transitions.

2.6.2 Proposed Solution

The lateral peak error will be sufficiently reduced if a farther point ahead of the vehicle on the reference path provides advanced information of curvature transitions. In addition, a closer look ahead reference point is required to compensate the centrifugal forces as well as a lateral deviation controller to guarantee the tracking preciseness.

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This study offers a simple method that improves stability and provides sufficient tracking accuracy to prevent the above-mentioned drawbacks.

The underlying foundation for modelling is built on previous studies (e.g. Bell, 1999; Bevly, 2001; Gartley, 2005). The goal of the proposed method is to track a reference path at a sufficiently high accuracy so that the distance between the middle of the rear wheels and the reference path always remains within the typical required tolerances of agricultural applications. It was assumed that a curvilinear reference path is planned by a higher level navigation planner, and the vehicle is equipped with proper instruments to determine its position and orientation with respect to the reference path frame. Thus, the controller on the vehicle can search the nearest point on the path and determine the lateral deviation of the vehicle from the path. A look-ahead reference point (LARP) is a point on the reference path at a specified curvilinear distance from the nearest point. The proposed LARP control method simply emulates natural actions of three virtual drivers over the nearest point and two look-ahead points on the desired path. The difference between the direction vectors of a look-ahead reference point and the nearest point mainly provides the curvature of the path in advance, and also provides correction for the centrifugal forces along the circular paths. Using multiple LARPs provides smoothness of the driving actions, and reduces the peak errors at the transition of partitions. The output of the LARP control is applied to the steer angle employing an EH-actuator which is linearised by a servo control loop.

Among the advantages of the proposed system are i) simple reference path representation, ii) computational simplicity, e.g., no integral, and iii) fewer position data

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requirements compared to the other methods. Further development is feasible to reach a certain level of maturity for a more detailed system. The goal is an approach that is convenient for agricultural applications such as spraying and seeding, and has a sufficient level of safety for travelling between crop rows.

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Chapter 3

3. MODELLING APPROACHES

3.1 Modelling Preliminaries

In order to predict and analyse the future states of the real system there is an absolute need for mathematical modelling. A proper model of the system can express the relations and behaviour in the system and the interactions between the sub-systems. Hence, this section introduces the fundamental relations and formulations needed to build a dynamic model of a vehicle in agricultural working conditions that have considerable skid and slip.

To form a structure for the sake of analysis and evaluation, first, each system must be analyzed independently to take into account the details which have significant effect on the behaviour of the system when the kinematics and kinetics of the whole system is considered (Senatore and Sandu, 2011).

For modelling the whole system four main sub-systems must be taken into account; the vehicle (upper moving body), tyre and tyre contact patch, sensor noise and delay, actuator saturation and lag as well as terrain irregularities. These are the least for the modelling of a vehicle tracking while in some research the controller act as a dynamic behaviour regulator to track the desired route while towed implement or trailer is attached and also the obstacles are assumed to be available and must be passed such that no crush or turn over occur.

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Although, vehicle behaviour can be controlled to behave in the region that formulation is straightforward and can be held in the linear region; the tyre interactions with the terrain surface is not that much routine to be modelled via a simple and short formula, especially when the slip and skid occur. In such cases the experiments must be carried out to determine the model that can well predict the effect of the travel on the unpaved road and give the required involved parameters within the system functionality. Wheel interaction with the soil that hardly behaves like a homogenous material has been a field of interest and has been studied in details since 1987 (Bakker et al. 1987) up to 2011 (Senatore and Sandu, 2011). Moreover, in the field there are unknown disturbances. In the present study the soil disturbance to be model and applied on the system is a load that acts in the modelling as a special mathematical function. Indeed, disturbance on the field is whatever that was not already taken into account and might alter the vehicle’s behaviour for tracking a desired route (Bell 1999).

A model that deliberately takes into account all the circumstances and forces is impossible (Bevly and Cobb 2010).

An accurate model of a steering system is expected to generate the same outcomes as the real vehicle on the actual field so that the conditions of the real system must be well perceived. On the other hand, in the majority of previous well known studies, it has been tried to come up with a system that is relatively simple and sufficiently precise (Bevly and Cobb 2010, Bakker et al 1987, Gartley 2005, Zhang and Qiu 2004, Fang et al. 2011)]. The last two terms introduce ambiguity that is undesirable for a systematic

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research. By simplifying the system for specific applications, minimal computational effort will be produced as was done by Senatore and Sandu (2011).

Furthermore, accuracy also indicates a proposed controller system, works at least in the same level as a human operator. The designed system might perform better than the previous proposed systems but an overview of the previous studies on the off-road automatic vehicle steering system denotes that each proposed method thus far stands for special conditions and limited range of parameter variations (Li. Et al 2009, and Reid et al. 2000). Although this study attempts to show the effectiveness of the proposed controller by means of evaluation over the same foundation leading to performance comparison regardless of whatever the outcome might be, rather than the prediction of the exact effects on the real set up since some processes on the real setup is not determined beforehand, however it is possible to have close results to the real set up via some correction gains (Derrick 2008) or some parameter modifications (Lenain et al. 2006).

A detailed description and discussion of the vehicle and terrain modelling will follow this section including the circumstances assumed prior to modelling.

3.2 Model of Vehicle Kinematics and Dynamics

An accurate model of the vehicle steering system represents all motions on the vehicle body. The model of a steering system without towed implement is quite straightforward since the perturbations on the system are less whereas they have serious impact on the system inasmuch as the response type of the system might easily change (Derrick,

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2008). Most likely they affect the vehicle body side slip angle which in turn alters the vehicle states to display inaccurate outcomes (Fang, et al. 2011)

A model that has been broadly used by the researchers is an 8 degree of freedom model of the vehicle that is designed to show the lateral, longitudinal, bounce, roll, pitch and yaw which are all assumed on the vehicle centre of gravity. Although the control point might be assumed elsewhere on the vehicle or the whole system body, the computational efficiency will not be affected by simple arithmetic that will be used for control point position determination.

One may notice that in off road vehicle steering analysis some variables such as aerodynamic (wind) force or suspension effect have no significance or involves fewer effects (Bell, 2000, and Kiencke and Nielsen, 2005).

A typical four wheel active front tyre steering vehicle may be accurately modelled by an 8 DOF model, but in almost all previous research studies, it has been common to simplify the 8 DOF model into 3 DOF to reduce system complexity without losing the main characteristics of the dynamic system (Bell, 1999; Bevly, 2001; Gartley, 2005; Derrick and Bevly, 2008; Fang, et al., 2011; Zhang and Qiu, 2004). The side view of the system is shown in Figure 1.

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3.3 Tyre model for vehicle dynamics

The main effective parameters within the steering system analysis and evaluation are the tyre interaction with the terrain surface. Indeed the friction coefficient between the tyre treads and the soil surface produces the force to act as a major quantity to govern the motion of the vehicle (Karkee, 2010). The mismatch between the simulation of a steering model and the actual test is caused by the fact that the tyre is not as circular as it is assumed. Besides, the faulty assumption regarding suspension and symmetric body motion pre-considerations such as roll and pitch motion neglecting load transfer discarding can be another reason to observe discrepancies between simulation and real experiment tests. Apart from that, the tire deforms in such a way that it adjusts itself to the terrain bed and therefore, the lower part of the tire becomes flat. This is the reason why the relaxation length was introduced by Senatore and Sandu (2011) to correct the previous formulation over the unpaved and paved road surfaces. Although a widely accepted tire model cannot be found in the literature (Karkee and Steward, 2010) and most likely it is due to the circumstances and application of the tyre study, it is possible to work in the region that has been commonly used in the controller design task in the

b

Figure 1. Side view of a typical agricultural vehicle with implement for material spreading dynamics having controller and position-sensor unit

Design and Development of an Auto-Steering System Control for Off-Road Vehicles